For any function that is continuous over the closed interval [a,b] and differentiable over the open interval (a,b), there exists a point c where the slope at that point equals the average rate of change from (a,b).
This is written as:
f'(c)= [f(b)-f(a)]/(b-a)
Ex: On the continuous interval [2,4], f(x)= x^2
This means there exists a point c where the slope at that point equals the average rate of change from 2 to 4.
f'(c)= [f(4)-f(2)]/(4-2)
= (8-4)/2
= 2
This is written as:
f'(c)= [f(b)-f(a)]/(b-a)
Ex: On the continuous interval [2,4], f(x)= x^2
This means there exists a point c where the slope at that point equals the average rate of change from 2 to 4.
f'(c)= [f(4)-f(2)]/(4-2)
= (8-4)/2
= 2